Climate change and resource scarcity pose increasingly difficult challenges for the aviation industry requiring a reduction in fossil fuel consumption. To address these problems and increase the efficiency of aircraft engines, some of their parts are now manufactured in one piece. For example, a rotor of the compressor stage of an airplane engine consist of a drum with a large number of blades and is called BluM. These structures are lightweight and feature low structural damping and high modal density. Their particular dynamic characteristics require sophisticated solutions for vibration mitigation of these structures.

This is precisely the starting point of this thesis. Based on a digital realization of piezoelectric shunt circuits, we provide a damping concept that is able to tackle the complex dynamics of bladed structures and to mitigate their vibrations. To this end, multiple digital vibration absorbers (DVAs) are used simultaneously. Two new strategies to tune these DVAs are proposed in the thesis, namely the isolated mode and mean shunt strategies. These strategies not only take advantage of the fact that multiple absorbers act simultaneously on the structure, but they also address the problem of closely-spaced modes. In order to target multiple families of BluM modes, these strategies are incorporated in a multi-stage shunt circuit. The concepts are demonstrated experimentally using two bladed structures with increasing complexity, namely a bladed rail and a BluM. Both methods exhibit excellent damping performances on multiple groups of modes. In addition, they prove robust to changes in the host structure which could, e.g., be due to mistuning. Thanks to their digital realization, DVAs are also easily adjustable.

Finally, this thesis reveals the parallel that exists between resonant piezoelectric shunts with a negative capacitance and active positive position feedback (PPF) controllers. Based on this comparison, a new H∞ norm-based tuning rule is found for a PPF controller. It is demonstrated using both numerical and experimental cantilever beams. To this end, a method that accounts for the influence of modes higher in frequency than the targeted one is developed.